Some results for range of random walk on graph with spectral dimension two
Kazuki Okamura
Abstract:We consider the range of the simple random walk on graphs with spectral dimension two. We give a form of strong law of large numbers under a certain uniform condition, which is satisfied by not only the square integer lattice but also a class of fractal graphs. Our results imply the strong law of large numbers on the square integer lattice established by Dvoretzky and Erdös (1951). Our proof does not depend on spacial homogeneity of space and gives a new proof of the strong law of large numbers on the lattice.… Show more
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